The DS was only used twice. Tarkin used it to destroy Alderaan, and he had already tested it with the destruction of Despayre. I don't think that the DS was built right after Palpy crowned himself. The DS which was bigger, was built in less than 4 years, with the design corrections. THE superlaser was designed int he maw, the only desgin that was available at the time of EP II was the superstructure. So for all that counts the DS of Ep II may have been jsut the hull, much like the Eye of Palpatine and such stuff.